Summary: Kinetics of Proton Migration in Liquid Water
Hanning Chen
and Gregory A. Voth
Center for Biophysical Modeling and Simulation and Department of Chemistry, UniVersity of Utah, Salt Lake
City, Utah 84112-0850
Noam Agmon*
The Fritz Haber Research Center and the Institute of Chemistry, The Hebrew UniVersity of Jerusalem,
Jerusalem 91904, Israel
ReceiVed: August 23, 2009; ReVised Manuscript ReceiVed: October 25, 2009
We have utilized multistate empirical valence bond (MS-EVB3) simulations of protonated liquid water to
calculate the relative mean-square displacement (MSD) and the history-independent time correlation function,
c(t), of the hydrated proton center of excess charge (CEC) with respect to the water molecule on which it has
initially resided. The MSD is nonlinear for the first 15 ps, suggesting that the relative diffusion coefficient
increases from a small value, D0, at short separations to its larger bulk value, D, at large separations. With
the ensuing distance-dependent diffusion coefficient, D(r), the time dependence of both the MSD and c(t)
agrees quantitatively with the solution of a diffusion equation for reversible geminate recombination. This
suggests that the relative motion of the CEC is not independent from the nearby water molecules, in agreement
with theoretical and experimental observations that large water clusters participate in the mechanism of proton
mobility.
Hydrogen bonds (HBs) in water are constantly breaking and